Answer
$$\langle -4,-2\rangle$$
Work Step by Step
$$\vec{a}+\vec{b}+\vec{c}+\vec{v}=\langle0,0\rangle$$
Solve for $\vec{v}$
$$\vec{v}=-\vec{a}-\vec{b}-\vec{c}=-\langle 6,-1\rangle-\langle -4,3\rangle-\langle 2,0\rangle$$
To combine vectors in component form, combine x and y components separately.
$$=\langle -6+4-2,1-3-0\rangle=\langle -4,-2\rangle$$
